Integrable Systems and Algebraic Geometry 2 Volume Paperback Set

A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.

Ron Donagi (Edited by), Tony Shaska (Edited by)

9781108785495, Cambridge University Press

Multiple-component retail product, published 2 April 2020

900 pages, 54 b/w illus. 14 tables
22.8 x 15.1 x 5 cm, 1.37 kg

Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. The work is split into two volumes, with the first covering a wide range of areas related to integrable systems, and the second focusing on algebraic geometry and its applications.

Volume 1: Integrable systems: a celebration of Emma Previator's 65th birthday Ron Donagi and Tony Shaska
1. Trace ideal properties of a class of integral operators Fritz Gesztesy and Roger Nichols
2. Explicit symmetries of the Kepler Hamiltonian Horst Knörrer
3. A note on the commutator of Hamiltonian vector fields Henryk ?o??dek
4. Nodal curves and a class of solutions of the Lax equation for shock clustering and Burgers turbulence Luen-Chau Li
5. Solvable dynamical systems in the plane with polynomial interactions Francesco Calogero and Farrin Payandeh
6. The projection method in classical mechanics A. M. Perelomov
7. Pencils of quadrics, billiard double-reflection and confocal incircular nets Vladimir Dragovi?, Milena Radnovi? and Roger Fidèle Ranomenjanahary
8. Bi-flat F-manifolds: a survey Alessandro Arsie and Paolo Lorenzoni
9. The periodic 6-particle Kac–Van Moerbeke system Pol Vanhaecke
10. Integrable mappings from a unified perspective Tova Brown and Nicholas M. Ercolani
11. On an Arnold–Liouville type theorem for the focusing NLS and the focusing mKdV equations T. Kappeler and P. Topalov
12. Commuting Hamiltonian flows of curves in real space forms Albert Chern, Felix Knöppel, Franz Pedit and Ulrich Pinkall
13. The Kowalewski top revisited F. Magri
14. The Calogero–Françoise integrable system: algebraic geometry, Higgs fields, and the inverse problem Steven Rayan, Thomas Stanley and Jacek Szmigielski
15. Tropical Markov dynamics and Cayley cubic K. Spalding and A. P. Veselov
16. Positive one-point commuting difference operators Gulnara S. Mauleshova and Andrey E. Mironov. Volume 2: Algebraic geometry: a celebration of Emma Previato's 65th birthday Ron Donagi and Tony Shaska
1. Arithmetic analogues of Hamiltonian systems Alexandru Buium
2. Algebraic spectral curves over Q and their tau-functions Boris Dubrovin
3. Frobenius split anticanonical divisors Sándor J. Kovács
4. Halves of points of an odd degree hyperelliptic curve in its jacobian Yuri G. Zarhin
5. Normal forms for Kummer surfaces Adrian Clingher and Andreas Malmendier
6. ?-functions: old and new results V. M. Buchstaber, V. Z. Enolski and D. V. Leykin
7. Bergman tau-function: from Einstein equations and Dubrovin–Frobenius manifolds to geometry of moduli spaces Dmitry Korotkin
8. The rigid body dynamics in an ideal fluid: Clebsch top and Kummer surfaces Jean-Pierre Françoise and Daisuke Tarama
9. An extension of Delsarte, Goethals and Mac Williams theorem on minimal weight codewords to a class of Reed–Muller type codes Cícero Carvalho and Victor G. L. Neumann
10. A primer on Lax pairs L. M. Bates and R. C. Churchill
11. Lattice-theoretic characterizations of classes of groups Roland Schmidt
12. Jacobi inversion formulae for a curve in Weierstrass normal form Jiyro Komeda and Shigeki Matsutani
13. Spectral construction of non-holomorphic Eisenstein-type series and their Kronecker limit formula James Cogdell, Jay Jorgenson and Lejla Smajlovi?
14. Some topological applications of theta functions Mauro Spera
15. Multiple Dedekind zeta values are periods of mixed Tate motives Ivan Horozov
16. Noncommutative cross-ratio and Schwarz derivative Vladimir Retakh, Vladimir Rubtsov and Georgy Sharygin.

Subject Areas: Mathematical physics [PHU], Algebraic geometry [PBMW], Differential calculus & equations [PBKJ]